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Iden%fying and Implemen%ng Lesson Goals to Measure Learning
in Mathema%cs
August 16, 2016
Mark Alcorn, Mathema%cs Coordinator, SDCOE
mark.alcorn@sdcoe.net @mark4math
Standards or Lesson Goals?
Learning Inten%ons • Understand the quality of the task determines what students learn about mathema%cs
• Understand the differences between measuring learning at the lesson level vs. the chapter/unit level
• Understand how using mathema%cs goals can allow teachers and students to measure learning throughout the lesson
Success Criteria • I can iden%fy characteris%cs of high-‐quality tasks • I can explain how lesson goals can guide and assess learning at the lesson level • I can iden%fy a next step for implemen%ng lesson goals in my classroom/school/district
Write a lesson goal for this task
• What types of tasks should students engage in to meet the demands of the California Mathema%cs Standards?
• What language could we use to define these tasks?
Doing Mathema%cs?
“Memorization” Tasks
What are the decimal and percent equivalents for the fractions and ?
Expected Student Response:
= .5 = 50%
= .25 = 25%
“Procedures With Connections” Tasks
Using a 10 x 10 grid, identify the decimal and percent equivalents of .
Expected Student Response:
Pictorial Fraction Decimal Percent
Lower-Level Demand
Cognitive Demands of Mathematical Instructional TasksHigher-Level Demand
a) On column will be 10% since there are 10 columns. So four squares is 10%. Then 2 squares is half a column and half of 10% which is 5%. So the 6 shaded blocks equal 10% plus 5% or 15%.
b) One column will be .10 since there are 10 columns. The second column has only 2 squares shaded so that would be one half of .10 which is .05. so the 6 shaded blocks equal .1 plus .05 which equals .15.
c) Six shaded squares out of 40 squares is which is equivalent to
Stein, M. & Smith, M. (1998) Mathematics Teaching in the Middle School. National Council of Teachers of Mathematics
“Procedures Without Connections” Tasks
Convert the fraction to a decimal and a percent.
Expected Student Response:
Fraction Decimal Percent
“Doing Mathematics” Tasks
Shade 6 small squares in a 4 x 10 rectangle. Using the rectangle, explain how to determine each of the following: a) the percent of area that is shaded, b) the decimal part of the area that is shaded, and c) the fractional part of area that is shaded.
One Possible Student Response:
Memoriza%on
Procedures without Connec%ons
Procedures with Connec%ons
Doing Mathema%cs
Some characteris%cs of a high-‐quality task
• Reflects high cognitive demand (Stein et. al., 1996)
• Allows multiple ways to enter the task and to show competence (Lotan, 2003)
• Provides access to a wide range of learners (Piggott, 2012)
• Encourages creativity and imaginative application of knowledge (Piggott, 2012)
• Exposes what students know and provides information for next steps (Hiebert, et. al., 1997)
• Encourages reflection and communication (Hiebert, et. al., 1997)
• Promotes connections between two or more representations (Lesh, Post & Behr, 1988)
• Leaves behind something of mathematical value (Hiebert, et. al., 1997)
Kevin is preparing for the Rock and Roll Marathon. In his training run, Kevin drinks 2/3 cup of water for every mile he runs. His water bottle holds 4 cups of water. How many miles can he run before his water runs out? Draw a picture or model first to represent the situa%on.
Rock and Roll Run
High-‐Level Task…now what? What will students understand about mathematics by the end of the lesson that they did not know at the start? Which students should I select to share their thinking?
Which students should share their strategy?
Grain size of mathema%cs Why is it harder to express mathematical understandings at the lesson level vs. chapter/unit level? http://math.serpmedia.org/5x8card/phil-daro-on-the-5x8-card.html
Implica%ons • Shift to chapter/unit collaborative planning regarding
mathematics content
• After this shift, what happens at the lesson level?
Kevin is preparing for the Rock and Roll Marathon. In his training run, Kevin drinks 2/3 cup of water for every mile he runs. His water bottle holds 4 cups of water. How many miles can he run before his water runs out? Draw a picture or model first to represent the situa%on.
Rock and Roll Run
Pre-‐Plan ques%ons that address the Standards for Mathema%cal Prac%ce
SMP #1 – Does your answer make sense? How do you know? SMP #2 – Could we have used another operation? SMP #3 – What would happen to the answer if we used a larger water bottle that holds 8 cups? How do you know? SMP #4 – How did you represent the quantities in the situation? SMP #5 – Which tools help represent the situation? SMP #6 – Does your solution make sense in this context? SMP #8 – What patterns did you notice in your picture? Note: Students will engage in additional SMPs beyond these identified as the focus of the lesson.
Lesson # ___ of ___Common Core Standards:1.
2.
3.
Lesson Goals (Learning Intentions):
Task:
Strategy Who and What Order
Standards for Mathematical Practice1 2 3 4 5 6 7 8
Question:
Question:
Question:Evidence of Learning (Success Criteria):
x x
Kevin drinks 2/3 cup of water for every mile he runs. His water bottle holds 4 cups of water. How many miles can he run before his water runs out?
Students will examine patterns in their drawing or model to determine the operation
How did you represent the quantities in the situation? What patterns did you notice in your picture?
BEFORE DURING BEFORE/DURING
Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
5.NF.7
Coach Isabella bought 8 pizzas for the hungry soccer team. Each member of the soccer team ate ½ pizza. How many people ate pizza? Explain how your sketch/model connects to your equation.
Shared student work is based on the goal
A lesson goal…why? • What rationale would you provide to encourage a colleague to consider setting a lesson goal in mathematics?
Lesson Goals in Primary Grades 4 children are sharing 3 candy bars so that everyone gets the same amount. How much candy bar can each child have?
Ideas for Implementa%on • Use a criteria to analyze the quality of mathema%cs tasks • Introduce the tool, “Ques%ons to support Engagement in the Standards for Mathema%cal Prac%ce” as a method to support student engagement with high-‐quality mathema%cs tasks
• Form lesson goals in mathema%cs based on 1-‐3 ques%ons from the above tool
• Encourage students to track their learning based on the lesson goal
Resources • Leinwand, Steven, Daniel J. Brahier, DeAnn Huinker, et. al. Principles to Ac.ons: Ensuring Mathema.cal Success for All. Reston, VA: NCTM 2014.
• Smith, Margaret S. and Mary Kay Stein. 5 Prac.ces for Orchestra.ng Produc.ve Mathema.cs Discussions. Reston, VA: NCTM, 2011.
Next Steps • Iden%fy 1-‐2 next steps for implemen%ng lesson goals in your classroom/school/district
Be prepared to share an idea with your colleagues
Upcoming Professional Learning Ge#ng Smarter about Tasks and Talk (2-‐day): October 4 & 25, January 24 & 27, February 23 & March 9 Advanced Tasks and Talk (1-‐day): October 6, October 13, December 13, or April 18 Teaching FracAons for Meaning and ApplicaAon (1-‐day): October 12 or February 14 Mark Alcorn -‐ mark.alcorn@sdcoe.net Twiker: @mark4math Web: www.sdcoe.net
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